Generalized Ellis-Bronnikov graphene wormhole

Abstract

In this paper, we investigate the spinless stationary Schrödinger equation for the electron when it is permanently bound to a generalized Ellis-Bronnikov graphene wormhole-like surface. The curvature gives rise to a geometric potential affecting thus the electronic dynamics. The geometry of the wormhole's shape is controlled by the parameter $n$ which assumes even values. We discuss the role played by the parameter $n$ and the orbital angular momentum on bound states and probability density for the electron.

arXiv comment9 pages, 6 figures, two columns

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• Geometrodynamics of a 2D Curved Surface due to a Constrained Quantum Particle via its Gravitational Dual: ${\mathcal{S}}^2$ Analytical Model Calculations